benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Two points A and B are given in the plane. A point X is called their [i]preposterous midpoint[/i] if there is a Cartesian coordinate system in the plane such that the coordinates o…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Two points AA and BB are given in the plane. A point XX is called their [i]preposterous midpoint[/i] if there is a Cartesian coordinate system in the plane such that the coordinates of AA and BB in this system are non-negative, the abscissa of XX is the geometric mean of the abscissae of AA and BB, and the ordinate of XX is the geometric mean of the ordinates of AA and BB. Find the locus of all the [i]preposterous midpoints[/i] of AA and BB. (K. Tyschu)
Plain-text mathematical notation (without MathML)
Two points A and B are given in the plane. A point X is called their  [i]preposterous midpoint[/i] if there is a Cartesian coordinate system in the plane such that the coordinates of A and B in this system are non-negative, the abscissa of X is the geometric mean of the abscissae of A and B, and the ordinate of X is the geometric mean of the ordinates  of A and B. Find the locus of all the [i]preposterous midpoints[/i] of A and B. 

(K. Tyschu)
Original LaTeX notation
Two points $A$ and $B$ are given in the plane. A point $X$ is called their  [i]preposterous midpoint[/i] if there is a Cartesian coordinate system in the plane such that the coordinates of $A$ and $B$ in this system are non-negative, the abscissa of $X$ is the geometric mean of the abscissae of $A$ and $B$, and the ordinate of $X$ is the geometric mean of the ordinates  of $A$ and $B$. Find the locus of all the [i]preposterous midpoints[/i] of $A$ and $B$. 

(K. Tyschu)

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
221a9105-862f-5721-8d09-f2053245148d
task_key
test--221a9105-862f-5721-8d09-f2053245148d
task_revision_id
1
config / split
/ test

Official source

initial import